package DP;

public class UniquePaths {
    public static void main(String[] args) {
        System.out.println(uniquePaths(3, 3));
    }

    // 方法一：求二叉树树叶结点个数
    public static int uniquePaths(int m, int n) {
        return dfs(1, 1, 3, 3);
    }

    static int dfs(int i, int j, int m, int n) {
        if (i > m || j > n) return 0;

        if (i == m && j == n) return 1;

        else return dfs(i + 1, j, m, n) + dfs(i, j + 1, m, n);
    }

    public static int uniquePaths2(int m, int n) {
        int dp[][] = new int[m][n];
        for (int i = 0; i < m; i++) {
            dp[i][0] = 1;
        }
        for (int i = 0; i < n; i++) {
            dp[0][i] = 1;
        }
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
            }
        }
        return dp[m-1][n-1];
    }


}
